# how can an Annual Percentage Rate (APR) of 26.70% be converted to a monthly rate?

Hello and Good Morning Everyone,

I am wondering how an Annual Percentage Rate (APR) of 26.70% be converted to a monthly rate.  Speaking hypothetically, I will put these numbers out here in order to capture or clarify my question.  An account has a balance of \$500 with an APR of 26.70%. Given this information, how much interest would be added to this balance within one month?

Thank you

George
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If they use Simple Interest for calculation (you need to ask them). Then 26.7% is 0.07..% per day, so the interest on \$500 for a 31 day month is \$0.37 per day or \$11.34 for the month.  Verify: \$500 x 26.7% = \$133.50 per year / 12 = \$11.13

I hope this helps.

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Also, if you need more precision (I typically do not), you need to know from the institution if interest is simple, compounded monthly, weekly or daily, in advance or in arrears.  The fine print on any statement will give you the exact daily rate for the APR.
Principal Software EngineerCommented:
For interest compounded monthly (the usual case for credit cards):

Take the log (any base) of the interest rate, in this case 1.267.  Log(10) 1.267 = .102777

Divide by the number of compounding periods, in this case 12.  .102777 / 12 = .008565

Take the antilog of that value.  antilog(10) 0.08565 = 1.019917

The monthly rate is that value less 1, in this case 1.9917 percent.

So for your example the \$500 becomes \$509.96.  Less  the original \$500, the interest is \$9.96 in the first month.

And this is why credit cards eat you alive if you don't pay them off every month.
Author Commented:
Hello and Good Afternoon Everybody,

Thank you for sharing  your calculations.  This is certainly good information to know.

George